g 0304 Paper

Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2010, Shanghai

Spatial Structures – Permanent and Temporary

November 8-12 2010, Shanghai, China

Flexible Mould for Precast Concrete Elements

Christian RAUN2, Mathias K. KRISTENSEN

2, Poul H. KIRKEGAARD

1*,

1*Associate Professor, Department of Civil Engineering, Aalborg University

Sohngaardsholmsvej 57. DK-9000, Denmark

[email protected]

2Department of Architecture & Design, Aalborg University, Denmark

Abstract

The present paper describes the development of a digitally controlled mould that

forms a double curved and fair surface directly from the digital CAD model. The

primary motivation for the development of the mould is to reduce the cost of

constructing double curved, cast elements for architecture, both in-situ cast and

modular. Today, such elements are usually cast in milled formwork that is expensive

and produces a lot of waste. Architects are often limited in their freedom of design by

the high costs of the existing methods and as a result, the possibilities for drawing and

evaluating complex shapes in architecture today, are not reflected in the build

architecture.

Keywords: Concrete mould, flexible mould, organic architecture, CNC milling.

1. Introduction

Complex freeform architecture is one of the most striking trends in contemporary

architecture. Today, design and fabrication of such structures are based on digital

technologies which have been developed for other industries (automotive, naval,

aerospace industry). Architecture differs from these traditional target industries of

CAD/CAM technology in many ways including aesthetics, statics, structural aspects,

scale and manufacturing technologies. It can be easy to develop a digital design by

computer tools, however the translation to a real piece of architecture can be very hard

and expensive. The traditional production methods available for free-form architecture

have a lack and architects and engineers are forced to simplify their designs. Production

of architectural freeform structures requires the segmentation into panels, which may be

either flat, single or double curved and produced in different building materials. Today,

methods for manufacturing freeform concrete formwork are available, and more are

being developed [1-4]. The most notable will be examined in this paper for verifying the

quality of the developed solution. The common way of producing unique elements is to

manufacture one mould for each unique element. This method has been made more

available by the development of faster CNC milling in cheaper materials, but since the

method is still labor intensive and produces a lot of waste, research is carried out in

several projects to find a solution, where one mould simply rearranges itself into a




variety of familiar shapes. Such a concept has natural limitations, but will fill a gap as a

complimentary technology to the existing. The core of the concept presented here is to

have a flexible surface manipulated into a given shape using a digital signal created

directly from the CAD drawing of the design. This happens fast, automatic and without

production of waste, and the manipulated surface is fair and robust, eliminating the need

for additional, manual treatment. Limitations to the possibilities of the flexible form are

limited curvature and limited level of detail, making it especially suited for larger,

double curved surfaces like facades or walls, where the curvature of each element is

relatively small in comparison to the overall shape. The present paper describes the

development of the flexible mould for production of precast thin-shell fiber-reinforced

concrete elements which can have a given form. The mould consists of pistons fixing

points on a membrane which creates the interpolated surface and is fixed to the form

sides in a way that allows it to move up and down.

2. Concrete casting techniques

Today, a number of technologies have emerged, that offers casting methods for a range

of purposes. On a large scale, the market is dominated by well known techniques such

as precast elements made from standard moulds and in-situ casting in standardized

modular systems. On a small scale, new methods for casting and new types of moulds

have emerged to meet the rising demand for customization and creation of curved

concrete architecture. Some of the methods for double curved moulds which have been

investigated related to the present project are mentioned below.

2.1 Milled foam moulds

The milled foam method represents the newest and the most economic version of

custom manufactured moulds, historically made by hand and recently milled in different

materials using CNC.

Fig. 1: Photo of a robot CNC-machine milling in a styropor material.

The advantage of foams in comparison to heavier materials is, that they are cheaper

compared on volume, they allow fast milling, and they are easy to manually alter and

fair after the milling process, that leaves a grooved surface texture. The main strength

of the method is that it can be used for very advanced geometry as long as it is possible

to de-mould the casted object. Further there is almost no curvature or detailing level




limitations besides that of the milling tool. Another clear advantage for this method is

that the entire surface is manufactured to tolerances. The weakness of the method is,

that it requires manual fairing and coating to a large extend, if the surface has to be of a

perfectly smooth, polished quality. For a large project, the formwork is extensive, and

after use it has to be thrown out, creating even more waste than was produced during

milling.

2.2 Textile formwork Casting in membrane formwork or textile moulds have been around for a long time. A

common feature for all objects that can be cast in this way is, that they must consist of

convex surfaces exclusively, since the method relies on the principle that all textiles

must be in tension caused by the viscous pressure. The final shape of the cast piece is a

result of the membrane's adaption to the pressure, like the shape of an inflated balloon.

The formwork is inexpensive in comparison to the surface area and totally smooth

surfaces can be achieved. Because of the limited use of material, little waste is

produced. Being inaccurate, the formwork can be produced relatively fast without the

use of advanced equipment. The inability to do anything else than convex forms is a

distinct limitation. Also, the only precisely controlled parts of the cast geometry, is

where the formwork have been fixed to its supports.

Fig. 2: Photo of a textile formwork.

2.3 Spray applied concrete

This method has been around for decades, but is still used for curved surfaces today. In

short, the concrete paste is mixed with chopped fiberglass in a spraying nozzle, and

applied to an underlying form with the reinforcement iron bars bend in place. After

application, the concrete surface is manually faired or kept rough. The fibers’ added to

the concrete serve to add extra strength, but more importantly to keep the newly applied

concrete in place. The method is mainly used for in-situ castings, and can form large

spans and surfaces in one continuous, structural piece, as the reinforcement is a

continuous structure as well.




The method is very labor intensive, as both the bending of reinforcement and the

application of concrete is a manual process. It is also very difficult to create perfectly

smooth surfaces, as the surface is finished off using hand tools.

Fig. 3: Photo showing spray applied concrete.

2.4 System based traditional formwork, PERI

PERI is a German producer of traditional scaffolding systems, but they have expanded

their product portfolio to include both flexible single curvature formwork and custom

double curved formwork. PERI specialty is that they use standard components for the

production of all their form work and both the single curvature flexible form and their

custom double curved forms are integrated into a complete and rationalized in-situ

system. They have also developed software that can automatically determine what parts

are needed based on a given geometry. It is a complete and reliable solution from

software to hardware, design to construction. The main weakness is that there is still

waste produced in the process of creating the double curved moulds, and that it is only

possible to create double curved surfaces of very small curvature.

Fig. 4: Photo showing PERI’s single curvature scaffolding.

The systems and methods shown above cover each their different aspects of freeform

architecture. Whether building scale or curvature is taken into consideration, there

seems to be a gap in scale from the textile and milled moulds to PERI’s large scale




buildings and the labor intensive, hard to fair spray applied concrete. PERI’s boards or

plywood sheets forced to create double curvature has a fairly small maximum curvature,

and it seems futile to use a precision tool like a CNC milling machine, with its

capability to produce very accurate and complex geometries, to create larger modules of

relatively small curvature without further detailing. When looking at this curvature

scale - smaller buildings created from a larger number of precast elements of familiar

scale and curvature, it seems such elements could be generated from a common tool, the

curvatures of which could be found between the maximum curvature of the force-bend

scaffolding from PERI and the small, complex curvatures possible by milled moulds. A

flexible tool could be competitive with foam milling in this area, if it were made, so that

no additional, manual treatment of cast elements or surface were needed, no waste

produced and production speed in comparison to equipment price were better. A tool for

creating modular solutions should come with a software or system to rationalize

production and communicate possibilities to architects. At the same time, the direct

connection between drawing and machine, as with the CNC miller, should be

established, to get an automated process. If a tool can be created to meet the criteria

stated above, it could help promote the construction of the freeform architecture that is

so commonly seen in digital architecture and competition drawings today, by offering

cheaper and more efficient custom building parts. It could help bring the build

architecture closer to the digital possibilities.

2.5 Flexible moulds

The most important aspect to consider when designing a flexible form is its limitations.

The wider the desired range of possible shapes, the more difficult and advanced the

construction will be. As discussed in the previous section, CNC milled foam moulds

will at some point of complexity be the most attractive solution, as they are able to mill

shapes that would be extremely hard to achieve by any other way of manipulating a

surface. It is also clear, that no matter how a surface is manipulated in a flexible form,

the very nature of the method results in a specialization in a common family of shapes.

For instance, if a flexible mould were to create a perfect box, it may be designed to take

different length, width and height, but because it needs specialized geometry like

corners, it would be unable to create a sphere with no corners. A flexible mould aiming

at the ability to do both, would possibly fail to achieve a perfect result in either case.

It all comes down to the fact, that every point on the surface of a flexible mould does

not have the ability to change from continuity to discontinuity, because that would

demand an infinitely high number of control points. Without an infinitely high number

of control points, the flexible form, therefore, has to aim at creating smooth, continuous

surfaces, the complexity of which must simply be governed by the number of control

points. It is then left to decide, what the least number of control points is, relative to the

properties of the membrane which will result in a mould design capable of achieving the

curvatures needed for most freeform building surfaces. The initial motivation for the

design of a flexible mould for double curved surfaces, was the encounter of other

attempts to come up with a functional design for such a form, and the market potentials

described in these projects. The technical difficulties and solutions defined in the

projects presented here have been the inspiration for our present design.




2.6 Membrane Mould

[1] presents a prototype for casting fiber reinforced polyester panels. The mould concept

is to have a flexible membrane manipulated by air filled balloons. The use of balloons

solves the problem of creating smooth bulges on a membrane with no stiffness in

bending, but it is hard to control the tolerances. The edge conditions are, however,

defined relatively precise by linear, stiff interpolators connected to rods and angle

control.

Fig. 5: Edge control by angle measurements [1].

Fig. 6: This edge control means that the panels can be joined to create a relatively

continuous surface [1].

2.7 North Sails

North Sails in North America produces custom cast sails in a digitally controlled,

flexible form that uses a principle, where stiff elements created a smooth surface

between points defined by digitally controlled actuators. They simply use what appears

to be a thick rubber or silicone membrane which has an even surface, since it is

supported by a large number of small, stiff rods placed close together underneath it. The

small rods are placed on top of larger rods connected to the actuators. This simple

system is possible because of the relatively small curvature in comparison to the mould

size. The mould is highly specialized and appears to have been extremely expensive,

but it is the best example of a flexible mould concept, that could easily be used to cast

concrete panels, and it has been the main inspiration for the principles used in our

mould.




Fig. 7: North Sails mould with numerous actuators.

3 Concept for a flexible mould

For a flexible mould, where only a set of points is defined, it is up to the membrane to

interpolate the surface between those points. Inspiration can be found in old boat

building techniques, where fair lines for a hull were drawn by bending a stiff member

through a defined set of points. The principle is that the curvature depends on the

distribution of internal forces. The internal forces will seek to be as low as possible, and

therefore, the member will take the shape, where the least deformation is needed to get

through the points. The principle of a stiff member interpolating a fair curve through

points is relatively easy to imagine in 2D, and for a 2D solution, this would beyond

doubt be the obvious choice for a “flexible curved ruler”. When drawing free form

NURBS curves in CAD programs, they are defined in much the same way, using

mathematical expressions that resemble the behavior of a stiff member. The curve

created by a physical member differs, depending on the stiffness. A stiffer member will

have a more equally distributed curvature, while a softer member will tend to have

higher peaks of curvature near the defined points, the softest possible being like a string

with all curvature at points and straight sections between. This bond between the

physical properties of a stiff member and the mathematical properties of a NURBS

curve can be applied to surfaces as well. If a plate interpolator can be made, that has an

equal stiffness for bending in all directions, but the freedom to expand freely in its own

plane, it would constitute a perfect 3D interpolator parallel to the well known 2D

solution, and the membrane presented by North Sails. Only, a membrane for a flexible

mould for architecture should be able to achieve much larger curvatures between each

actuator, then the solution of North Sails. To function as a surface suitable for casting

concrete or other substances against without the need for further manual treatment, it

should be durable and maintain a perfectly smooth and non-porous surface as well. A

membrane with these properties has been developed for this project, and it is the core of

the flexible mould invention.




Fig. 8: Pictures from testing the membrane principle. The membrane is fixed to

the table around the edges, and supported by a single 6cm high rod in the center.

The curvature can be seen to be evenly distributed around the support, and the

membrane has a smooth curved cross section over the point support.

The number of actuators in a row defines the precision and possible complexity of the

surface. A smaller number of actuators require a stiffer membrane and less control, a

larger number means softer membrane and better control. In this way, the amount of

actuators needed to depend on the complexity of the surface.




Fig. 9: Illustration of a surface deformed by 3, 4 and 5 actuators.

Five actuators in a section have been chosen not only because of the finer control, but

also because the coherence between the NURBS surfaces in a CAD drawing and the

physical shape of the membrane is better. The smaller leaps between the pistons mean

less deflection caused by the viscous pressure, and most important, the edge conditions

in a 5x5 configuration is less affected by the deflection elsewhere on the membrane,

then they are with the 4x4, which is important to ensure similar edges on different

panels, so that they can meet up nicely.

3.1 Fixation of pistons to membrane

Because the membrane is elastic and pistons are fixed in one position, the pistons

cannot be fixed to a defined point underneath the membrane. Both membrane and

pistons have to be fixed to a third system of sliding, bendable rods situated under the

membrane, which allows the membrane to flex freely in its own plane, while still being

fixed vertically as defined by the actuators. Since the upper limit for membrane stiffness

is defined by the membrane itself, this underlying system is fixed to the membrane in

many points to create additional stiffness to further reduce deflection from viscous

pressure.

Fig. 10: The structure connecting the membrane to the actuators consists of

spring steel members that are allowed to slide in both directions to obtain the

movements of the flexible membrane. The system is designed to ensure, that the

surface of the membrane has a constant offset from the surface defined by the

actuator heads.




3.2 Edge control

Curvature in the membrane is created by moments caused by the deflection of it. Along

the edges, no bending moment is applied in the direction perpendicular to the edge, and

therefore one has to be applied to ensure double curvature at the edges. For that reason,

handles has been applied to the underlying system. The handles are controlled

manually, at least on the first prototype, and they are forced into position and fixed after

the actuators have moved the membrane. These handles also serve the purpose of

safeguarding, that the inclination along the edges of the membrane is comparable to that

of the cast element next to it, to obtain an overall smooth surface.

Fig. 11: Principle drawing showing the pistons connected to the underlying rod

system, handles and scales for controlling the edge angle precisely and flexible

side scaffolding allowing for custom outline and edge angles of the cast

element.

3.3 Functionality and limitations

The mould can take any digitally defined shape within its limitations within one minute

from the execution of a program reading 25 surfaces coordinates directly from the CAD

design file. Once the actuator pistons have taken their positions, the handles must be

adjusted manually, one by one, to a fixed angle calculated by the program and

printed/shown. This will take a few minutes, as there are twenty handles around the

circumference. The main limitation of the mould is its maximum curvature. It is defined

by the construction of the membrane, and for the prototype, it is approximately a radius

of 1.5m. The whole system can of cause be scaled to achieve smaller radii. The

maximum curvature is for a double curved area with the given curvature in both

directions. For single or almost single curvature, smaller radii are possible, but the

performance has yet to be tested. Another limitation is that the surface designed has to

fit within the 1.2m x 1.2m x 0.3 m which is the box defined by the pistons. This box is

adequate to create a square piece of a sphere as big as the mould, with a radius of

1.44m. For most of the freeform architectural references, these limitations mean, that it

is still conceivable to produce the larger part of the surface.




Fig. 12: Perspective, showing the mould design, the top frame is for mounting

flexible side scaffolding, and it further supports the system for fixating the side

handles.

The flowing illustrations explain how the flexible mould can be used from design to

production of freeform architecture.

Fig. 13: Double curved surface , a subdivision of surface and validation of

subdivision

Fig. 14: Positioning of actuators, adjusting edge angles and mounting

mould sides.

Fig. 15: Pouring filling, single or double sided moulds and of mounting

elements




‘

Fig. 14: Computer rendering of a wall made up of elements produced with

the double sided mould technique.

4 Conclusions

Complex freeform architecture is one of the most striking trends in contemporary

architecture. Today, design and fabrication of such structures are based on digital

technologies which have been developed for other industries (automotive, naval,

aerospace industry). The present paper has presented traditional production methods

available for free-form architecture which force architects and engineers to simplify

their designs. Further the paper has described the development of a flexible mould for

production of precast thin-shell fiber-reinforced concrete elements which can have a

given form. The mould consists of pistons fixing points on a membrane which creates

the interpolated surface and is fixed to the form sides in a way that allows it to move up

and down. The main focus for the development has been on concrete facade elements,

but a flexible, digitally controlled mould can be used in other areas as well. Throughout

the project interest has been shown to use the mould for composites as well, and among

other ideas are the idea of casting acoustic panels, double curved vacuum formed veneer

and even flexible golf courses.

References

[1] Pronk, A., Rooy, I. V and Schinkel, P. Double-curved surfaces using a membrane

mould. Eds. Domingo A and Lázaro C. IASS Symposium 2009. Evolution and

trends in design, analysis and construction of shell and spatial structures. 2009:

618-628

[2] Helvoirt, J. Een 3D blob huid’ Afstudeerverslag 3370, Technische Universiteit

Eindhoven, 2003

[3] Boers, S. Optimal forming, http://www.optimalforming.com, Checked on the 30th

of June 2010

[4] Guldentops, L., Mollaert, M., Adriaenssens, S., Laet, L. and Temmerman, N.D

Textile formwork for concrete shells. IASS Symposium 2009. Evolution and trends

in design, analysis and construction of shell and spatial structures. 2009: 1743-

1754

g 0304 Paper

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